I had this same issue. My partner was in Nevada, and I live in California. The LLC was formed in the state of Nevada.
I tried opening a bank account on my own in California, I was told that my partner has to be present as well.
Because I was very persistent to find a solution, I had the opportunity to speak to the manager of the bank, and what we ended up doing is while I was in the bank, Chase in California sent a set of documents to the manager of a Chase bank in Nevada, thus both of the partners being present, one manager communicating with the other manager at the same time.
In conclusion it may work depending on the bank, also depending on the states you are in, because different states have different rules and regulations, also it matters the percentage of partnership. For example, if one partner has a minority share, again depending on the state and regulations, they may not have to be present, and the partner with higher percentage of the company can open up a bank account.
It's a very tricky situation, and I would say after you speak to multiple banks, it might be better to fly to the state where the LLC was formed and open the bank account there because the hassle might not be worth it. It worked for me, but each situation, bank, state, and partnership is different.
Good luck